I know this is a frequent problem, I myself confronted with this problem many times, yet somehow each Autocad dataset I received is different (although they're from the same area). To some data, the projection I gave them worked perfectly, and in this case it didn't.
So, I've recently received some AutoCad data. Converted them in ArcMap. They are missing spatial reference. But I know their location. They're suppose to be in a specific city in Romania.
So first thing I did, I gave them the Stereo 70 projection (Romania's national projection), I assumed this is the projection they were created in, the data gets somewhere in the middle of the Mediterranean Sea. Second thing I tried is is giving them WGS84, and they got somewhere in the Atlantic Ocean ;)
PS: I use ArcGIS 10.1
PS2: I've tried all 3 conversion methods (I know) in ArcMap.
PS3: The autocad data came with no spatial reference. I only know they should be in a specific city.